It is an important me thod tha t the exact so lutions of the heat conduction equations test the correctness o f the num er ica l so lutions. M eanwh ile, the sam e im po rtant is to use the nume rical so lutions ana ly zing the exact so lu tions for perfect resu lts. The hea t conduction equa tion w as so lved using based ce ll fin ite vo lum em ethod and the secondary order upw ind schem e in structured m esh. Three examp les are g iven show ing up the deficiency o f the exact solution o f the class ica l heat conduction equation in the paper. And, the inte rnal relation and the com plem entarities be tw een the exac t and the num erical so lutions are discussed